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How Are Shocks to Trend and Cycle Correlated? A Simple Methodology for Unidentified Unobserved Components Models

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  • Daisuke Nagakura

    (Institute for Monetary and Economic Studies, Bank of Japan (E-mail: daisuke.nagakura@boj.or.jp))

Abstract

In this paper, we propose a simple methodology for investigating how shocks to trend and cycle are correlated in unidentified unobserved components models, in which the correlation is not identified. The proposed methodology is applied to U.S. and U.K. real GDP data. We find that the correlation parameters are negative for both countries. We also investigate how changing the identification restriction results in different trend and cycle estimates. It is found that estimates of the trend and cycle can vary substantially depending on the identification restrictions imposed.

Suggested Citation

  • Daisuke Nagakura, 2008. "How Are Shocks to Trend and Cycle Correlated? A Simple Methodology for Unidentified Unobserved Components Models," IMES Discussion Paper Series 08-E-24, Institute for Monetary and Economic Studies, Bank of Japan.
  • Handle: RePEc:ime:imedps:08-e-24
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    File URL: http://www.imes.boj.or.jp/research/papers/english/08-E-24.pdf
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    References listed on IDEAS

    as
    1. Arabinda Basistha, 2007. "Trend-cycle correlation, drift break and the estimation of trend and cycle in Canadian GDP," Canadian Journal of Economics, Canadian Economics Association, vol. 40(2), pages 584-606, May.
    2. Zarnowitz, Victor & Ozyildirim, Ataman, 2006. "Time series decomposition and measurement of business cycles, trends and growth cycles," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1717-1739, October.
    3. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, June.
    4. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
    5. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    6. Charles Nelson & Eric Zivot, 2000. "Why are Beveridge-Nelson and Unobserved-Component Decompositions of GDP so Different?," Econometric Society World Congress 2000 Contributed Papers 0692, Econometric Society.
    7. Kosei Fukuda, 2007. "Are trend and cycle innovations uncorrelated? International evidence," Applied Economics Letters, Taylor & Francis Journals, vol. 14(12), pages 923-926.
    8. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-227, June.
    9. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
    10. Peter K. Clark, 1987. "The Cyclical Component of U. S. Economic Activity," The Quarterly Journal of Economics, Oxford University Press, vol. 102(4), pages 797-814.
    11. James C. Morley & Charles R. Nelson & Eric Zivot, 2003. "Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different?," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 235-243, May.
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    Cited by:

    1. Tara Sinclair & Yeuqing Jia, 2010. "Permanent and Transitory Macroeconomic Relationships between China and the Developed World," Working Papers 2010-08, The George Washington University, Institute for International Economic Policy.

    More about this item

    Keywords

    Business Cycle Analysis; Trend; Cycle; Permanent Component; Transitory Component; Unobserved Components Model;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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